๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

A new method of calculation in the Fractional Quantum Hall Effect regime

โœ Scribed by Bentalha, Zine ;Moumen, Larabi ;Ouahrani, Tarik

Book ID
125332100
Publisher
Walter de Gruyter GmbH
Year
2014
Tongue
English
Weight
301 KB
Volume
12
Category
Article
ISSN
2391-5471

No coin nor oath required. For personal study only.

โœฆ Synopsis

The electron-electron and electron-background interaction energies are calculated analytically for systems with up to N = 6 electrons. The method consists of describing the position vectors of electrons using complex coordinates and all the interaction energies with complex notation, whereby simplifications become possible. As is known, in this type of calculation, complicated expressions involving integrals over many variables are encountered and the trick of using complex coordinates greatly facilitates the exact calculation of various quantities. Contrary to previous analytical calculations, using complex coordinates avoids complicated trigonometric functions from appearing in the integrand, simplifying the exact evaluation of the integrals. The method we have used can be straightforwardly extended to larger systems with N > 6 electrons.

๐Ÿ“œ SIMILAR VOLUMES

A quantum dot in the fractional quantum
A quantum dot in the fractional quantum Hall regime
โœ Jari M. Kinaret ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 317 KB

In this article we discuss conductance through a quantum dot in the fractional quantum Hall regime. We argue that in the intermediate temperature regime (F~ .~ kT ~ A) many-body coherence strongly suppresses the conductance well below the integer regime values. In particular, we find that in the u =

Mesoscopic effects in the fractional qua
Mesoscopic effects in the fractional quantum Hall regime
โœ Michael R. Geller; Daniel Loss ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 72 KB

Edge states of the quantum Hall uid provide an opportunity to study mesoscopic e ects in a highly correlated electron system that is both experimentally accessible and theoretically tractable. In this paper we review recent work on the persistent current and Aharonov-Bohm magnetoconductance oscillat

Single-electron tunneling in the fractio
Single-electron tunneling in the fractional quantum Hall effect regime
โœ C.W.J. Beenakker; B. Rejaei ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 562 KB

A recent mean-field approach to the fractional quantum Hall effect (QHE) is reviewed, with a special emphasis on the application to single-electron tunneling through a quantum dot in a high magnetic field. The theory is based on the adiabatic principle of Greiter and Wilczek, which maps an incompres